Downlink Precoding Research Articles

Reconfigurable Massive MIMO: Harnessing the Power of the Electromagnetic Domain for Enhanced Information Transfer

The capacity of commercial massive multiple-input multiple-output (mMIMO) systems is constrained by the limited array aperture at the base station, and cannot meet the everincreasing traffic demands of wireless networks. Given the array aperture, holographic MIMO with infinitesimal antenna spacing can maximize the capacity, but is physically unrealizable. As a promising alternative, reconfigurable mMIMO is proposed to harness the unexploited power of the electromagnetic (EM) domain for enhanced information transfer. Specifically, the reconfigurable pixel antenna technology provides each antenna with an adjustable EM radiation (EMR) pattern, introducing extra degrees of freedom for information transfer in the EM domain. In this article, we present the concept and benefits of availing the EMR domain for mMIMO transmission. Moreover, we propose a viable architecture for reconfigurable mMIMO systems, and the associated system model and downlink precoding are also discussed. In particular, a three-level precoding scheme is proposed, and simulation results verify its considerable spectral and energy efficiency advantages compared to traditional mMIMO systems. Finally, we further discuss the challenges, insights, and prospects of deploying reconfigurable mMIMO, along with the associated hardware, algorithms, and fundamental theory.

Distributed Downlink Precoding for Cell-Free Massive MIMO: A Quasi-Neural Network Approach

Distributed Downlink Precoding for Cell-Free Massive MIMO: A Quasi-Neural Network Approach

One-Bit Downlink Precoding for Massive MIMO OFDM System

Massive multiple-input multiple-output (MIMO) is a key technology in next generation wireless communication. However, the increasing number of radio frequency (RF) chains results in higher cost and power consumption. Given that hundreds or even thousands of transmit antennas are equipped at the base station (BS), low resolution digital-to-analog converters (DACs) are preferred to reduce the power consumption on both DACs and power amplifiers (PAs). Currently, there have been some studies about the application of low-resolution DACs for single-carrier systems. For multi-carrier systems, this problem hasn’t been fully investigated. This paper aims to design a 1-bit downlink precoding algorithm for massive multi-user MIMO orthogonal frequency division multiplexing (OFDM) systems. A nonlinear precoding algorithm is proposed, which can address the non-convex optimization problem with discrete output constraint and guarantee convergence. Meanwhile, the proposed algorithm factors in the different path-losses experienced by different users. Furthermore, some approximation schemes can be applied to bring down the computational complexity of the proposed algorithm further. Simulation results illustrate that our algorithm performs the best among other nonlinear precoding methods in OFDM systems.

Two-Timescale-Based Beam Training for RIS-Aided Millimeter-Wave Multi-User MISO Systems

Reconfigurable intelligent surfaces (RISs), as a promising technology for 6 G communications, have received considerable attention. Herein, we investigate the downlink precoding in the RIS-aided millimeter-wave (mmWave) multi-user multiple-input single-output (MU-MISO) system, where the access point (AP) uses hybrid digital and analog precoders. Due to the constraints of practical hardware and the difficulty of acquiring channel state information, we consider codebook-based passive beamforming and analog beamforming, and then formulate the downlink precoding problem as a mixed-integer nonlinear programming (MINLP) problem. To solve this NP-hard MINLP problem with low channel estimation overheads, we investigate beam training for the codebook-based passive beamforming and analog beamforming, and the MINLP problem is then reduced to a traditional MU-MISO precoding problem. To further reduce the beam training overheads, we propose a two-timescale-based beam training (TT-BT) algorithm. We prove that the TT-BT algorithm achieves the maximum codebook-based passive and analog beamforming gain. To avoid the limitations imposed the use of the TT property, we design the analog precoder by aligning the analog beamforming to RISs. Moreover, we characterize the rate loss due to codebook-based quantization. Compared with the empirical BT (EBT) algorithm, the proposed TT-BT algorithm achieves better performance with significantly lower training and feedback overheads.

Downlink Precoding for Cell-Free FBMC/OQAM Systems With Asynchronous Reception

Downlink Precoding for Cell-Free FBMC/OQAM Systems With Asynchronous Reception

A Statistical Linear Precoding Scheme Based on Random Iterative Method for Massive MIMO Systems

In this paper, the random iterative method is introduced to massive multiple-input multiple-output (MIMO) systems for the efficient downlink linear precoding. By adopting the random sampling into the traditional iterative methods, the matrix inversion within the linear precoding schemes can be approximated statistically, which not only achieves a faster exponential convergence with low complexity but also experiences a global convergence without suffering from the various convergence requirements. Specifically, based on the random iterative method, the randomized iterative precoding algorithm (RIPA) is firstly proposed and we show its approximation error decays exponentially and globally along with the number of iterations. Then, with respect to the derived convergence rate, the concept of conditional sampling is introduced, so that further optimization and enhancement are carried out to improve both the convergence and the efficiency of the randomized iterations. After that, based on the equivalent iteration transformation, the modified randomized iterative precoding algorithm (MRIPA) is presented, which achieves a better precoding performance with low-complexity for various scenarios of massive MIMO. Finally, simulation results based on downlink precoding in massive MIMO systems are given to show the system gains of RIPA and MRIPA in terms of performance and complexity.

ADMM Based Symbol-Level Precoding for MU-MISO Downlink With Low-Resolution DACs

In this letter, we investigate the problem of symbol-level precoder design with low-resolution digital-to-analog converters (DACs) to implement wireless multiuser multiple-input single-output (MISO) downlink communications. Specifically, we aim to maximize the minimum distance between the noise-free received signal and its decision boundaries via a min-max fairness design. Due to the nondifferentiable objective and finite-alphabet constraint, the problem is NP-hard and difficult to tackle. To handle this problem, we first reduce the dimension of the variables by solving a relaxed problem. Then, the problem is transformed to a smoothed form which can be efficiently solved using the alternative direction method of multipliers (ADMM)-based framework. In addition, we propose a closed-from solution based on majorization-minimization method to provide a low-complexity near-optimal solution. We further provide the convergence and computational complexity analyses, and validate the performance by simulations.

Deep Learning for Channel Sensing and Hybrid Precoding in TDD Massive MIMO OFDM Systems

This paper proposes a deep learning approach to channel sensing and downlink hybrid beamforming for massive multiple-input multiple-output systems operating in the time division duplex mode and employing either single-carrier or multicarrier transmission. The conventional precoding design involves a two-step process of first estimating the high-dimensional channel, then designing the precoders based on such estimate. This two-step process is, however, not necessarily optimal. This paper shows that by using a learning approach to design the analog sensing and the hybrid downlink precoders directly from the received pilots without the intermediate high-dimensional channel estimation, the overall system performance can be significantly improved. Training a neural network to design the analog and digital precoders simultaneously is, however, difficult. Further, such an approach is not generalizable to systems with different number of users. In this paper, we develop a simplified and generalizable approach that learns the uplink sensing matrix and downlink analog precoder using a deep neural network that decomposes on a per-user basis, then designs the digital precoder based on the estimated low-dimensional equivalent channel. Numerical comparisons show that the proposed methodology results in significantly less training overhead and leads to an architecture that generalizes to various system settings.

Combining Reciprocity and CSI Feedback in MIMO Systems

Reciprocity-based time-division duplex (TDD) Massive MIMO (multiple-input multiple-output) systems utilize channel estimates obtained in the uplink to perform precoding in the downlink. However, this method has been criticized of breaking down, in the sense that the channel estimates are not good enough to spatially separate multiple user terminals, at low uplink reference signal signal-to-noise ratios, due to insufficient channel estimation quality. Instead, codebook-based downlink precoding has been advocated for as an alternative solution in order to bypass this problem. We analyze this problem by considering a "grid-of-beams world" with a finite number of possible downlink channel realizations. Assuming that the terminal accurately can detect the downlink channel, we show that in the case where reciprocity holds, carefully designing a mapping between the downlink channel and the uplink reference signals will perform better than both the conventional TDD Massive MIMO and frequency-division duplex (FDD) Massive MIMO approach. We derive elegant metrics for designing this mapping, and further, we propose algorithms that find good sequence mappings.

Robust Downlink Precoding for LEO Satellite Systems With Per-Antenna Power Constraints

Downlink precoding has been widely accepted as a crucial technique in low-earth-orbit (LEO) satellite communications due to its advantages in improving the space division multiplexing capability and enhancing spectrum efficiency. Because of the strong spatial directivity in the satellite channels, the downlink precoder can be efficiently designed based on the angle of departure (AoD)-based channel state information (CSI). However, acquiring perfect AoD-based CSI is challenging due to the angle estimation error and attitude jitter of the LEO satellites. In light of this, this paper investigates the precoder design for the LEO satellite downlinks with imperfect AoD-based CSI. For robust design, we treat the angle deviations of each user as random variables, which are supposed to exhibit a particular distribution, then integrate them within a certain range to achieve the robustness of the proposed downlink precoder against the angle mismatch. Instead of using the sum-power constraint on the transmit antennas, we adopt a more realistic per-antenna power constraint (PAPC). Accordingly, we formulate the problem to maximize the ergodic sum rate of the system. By leveraging the corresponding Lagrangian formulation and identifying the optimal precoder structure as the solution to a generalized eigenvalue problem, an iterative algorithm for the robust precoder design is derived. To reduce the computational complexity, a low-complexity version of the proposed algorithm is implemented based on deep learning techniques to meet the high demand for real-time applications in LEO satellite systems. Simulation results verify the effectiveness of the proposed precoding approach.

Angle-Based Downlink Beam Selection and User Scheduling for Massive MIMO Systems

The next-generation cellular system operating in millimeter-wave (mm-Wave) frequencies requires different signal processing schemes from the legacy LTE system. Among these, beam management aligns the transmitter-receiver pairs with narrow beams and serves as an essential initial acquisition procedure. This paper introduces a novel angle-based downlink precoding strategy, including beam selection and user scheduling for a full dimension (FD) MIMO-OFDM system. The highly directional mm-Wave channel allows the system to perform user/beam scheduling rather than pure user scheduling during the precoding process. A beam-based receive matrix eliminates the remaining intra-cell interference caused by overlapped beams. The performance analysis proves the superiority of the proposed precoding and scheduling strategies over the conventional technique.

Downlink Precoding for DP-UPA FDD Massive MIMO via Multi-Dimensional Active Channel Sparsification

In this paper, we consider user selection and downlink precoding for an over-loaded single-cell massive multiple-input multiple-output (MIMO) system in frequency division duplexing (FDD) mode, where the base station is equipped with a dual-polarized uniform planar array (DP-UPA) and serves a large number of single-antenna users. Due to the absence of uplink-downlink channel reciprocity and the high-dimensionality of channel matrices, it is extremely challenging to design downlink precoders using closed-loop channel probing and feedback with limited spectrum resource. To address these issues, a novel methodology – active channel sparsification (ACS) – has been proposed recently in the literature for uniform linear array (ULA) to design sparsifying precoders, which substantially reduces channel feedback overhead. Pushing forward this line of research, we aim to facilitate the potential deployment of ACS in practical FDD massive MIMO systems, by extending it from ULA to DP-UPA with explicit user selection and making the current ACS implementation simplified. To this end, by leveraging Toeplitz matrix theory, we start with the spectral properties of channel covariance matrices from the lens of their matrix-valued spectral density function. Inspired by these properties, we extend the original ACS using scalar-weight bipartite graph representation to the matrix-weight counterpart. Building upon such matrix-weight bipartite graph representation, we propose a multi-dimensional ACS (MD-ACS) method, which is a generalization of original ACS formulation and is more suitable for DP-UPA antenna configurations. The nonlinear integer program formulation of MD-ACS can be classified as a generalized multi-assignment problem (GMAP), for which we propose a simple yet efficient greedy algorithm to solve it. Simulation results demonstrate the performance improvement of the proposed MD-ACS with greedy algorithm over the state-of-the-art methods based on the QuaDRiGa channel models.

Robust Precoding for 3D Massive MIMO Configuration With Matrix Manifold Optimization

This paper investigates robust downlink precoding for three-dimensional (3D) massive multi-input multi-output (MIMO) configuration with matrix manifold optimization. Starting with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> channel model, we formulate the robust precoder design to maximize an upper bound of ergodic weighted sum-rate under a total power budget. We derive the generalized eigenvector structure for optimal precoder with matrix manifold optimization. However, since the precoding of multiple users is coupled in the structure, we maximize the objective function for each user in alternation and prove the solution of each individual problem is the generalized eigenvector corresponding to the maximum generalized eigenvalue. In accordance with this, we design an iterative algorithm and present its convergence analysis. Furthermore, we propose a Riemannian conjugate gradient (RCG) method to solve the generalized eigenvalue problem (GEP) for higher efficiency in the precoder design algorithm.

Downlink Precoding for Hybrid Fully Connected Linear Subarrays in mmWave With Rainfall Scattering and Hardware Impairments

In this treatise, we propose to design a transmit precoder at the base station (BS) for a hybrid fully connected sub-array (FCSA) architecture based on gradient projection (GP) and alternating minimization techniques. A random complex multiplicative factor comprehensively models the non-ideal nature of the power amplifier (PA), data converters (ADCs/DACs), and phase shifters (PSs) used in the transmitter radio frequency (RF) chain at the BS with the ideal mmWave channel. An effective noise term in the received signal with impairments is introduced, and the power of the same is derived. The effect of scattering of mmWave due to rainfall is taken into consideration. Two separate cases with the above-discussed impairments of (A) single user (SU) multiple-input multiple-output (MIMO) system and (B) multi-user MIMO (MU-MIMO) system are conceived. Both perfect and imperfect knowledge of the scattering parameters is considered. A linear minimum mean square error (LMMSE) channel estimation with the above impairments at the BS in the presence of rainfall scattering is performed. For both SU-MIMO and MU-MIMO systems, the spectral efficiency (SE) is evaluated for different rainfall rates at two carrier frequencies, viz. 38 GHz and 75 GHz. The channel estimate&#x2019;s mean square error (MSE) for ideal and hardware impaired systems is evaluated at various rainfall rates. The performance of channel estimation is evaluated with numerical simulation.

Low-Resolution Precoding for Multi-Antenna Downlink Channels and OFDM.

Downlink precoding is considered for multi-path multi-input single-output channels where the base station uses orthogonal frequency-division multiplexing and low-resolution signaling. A quantized coordinate minimization (QCM) algorithm is proposed and its performance is compared to other precoding algorithms including squared infinity-norm relaxation (SQUID), multi-antenna greedy iterative quantization (MAGIQ), and maximum safety margin precoding. MAGIQ and QCM achieve the highest information rates and QCM has the lowest complexity measured in the number of multiplications. The information rates are computed for pilot-aided channel estimation and a blind detector that performs joint data and channel estimation. Bit error rates for a 5G low-density parity-check code confirm the information-theoretic calculations. Simulations with imperfect channel knowledge at the transmitter show that the performance of QCM and SQUID degrades in a similar fashion as zero-forcing precoding with high resolution quantizers.

HF Skywave Massive MIMO Communication

In this paper, we investigate massive multi-input multi-output (MIMO) high frequency (HF) skywave communications. We first introduce a model for HF skywave massive MIMO channels within the orthogonal frequency division multiplexing transmission framework by using the matrix of sampled steering vectors. Considering the large antenna array aperture and increased signal bandwidth, the effect of the propagation delay across the large-scale antenna array cannot be ignored, and thus the steering vectors vary across different subcarriers. Specifically, we derive a wideband beam based channel model and show that the beam domain statistical channel state information (CSI) is frequency-independent. Then, we consider minimum mean-squared error (MMSE) based uplink receiver and downlink precoder with perfect CSI at the base station (BS). With a large number of antennas at the BS, the sum-rate can be asymptotically increased proportionally to the number of user terminals (UTs) while the transmit power per UT is scaled down inverse-proportionally to the number of antennas. In order to reduce the design complexities of the MMSE receiver and precoder, we derive a polynomial expansion based design using a deterministic equivalent. Simulation results demonstrate very significant performance advantages of the proposed HF skywave massive MIMO system.

Downlink transmission and channel estimation for cell-free massive MIMO-OFDM with DSDs

In a cell-free massive MIMO system, multiple users arrive at multiple access points at separate times, while in an OFDM system, different delays can be equivalent to delay spread differences (DSDs). Since DSDs are not all the same, in the downlink transmission process, it is necessary to consider its impact on transmission techniques, such as channel estimation and downlink precoding. In this paper, aiming at the performance loss caused by DSDs in cell-free massive MIMO-OFDM system, we propose a multi-RB precoding optimization algorithm that maximizes the downlink sum rate. We derive the sum rate maximization problem into an iterative second-order cone programming form to achieve convex approximation. Then, considering the impact of DSDs on the accuracy of cell-free massive MIMO-OFDM channel estimation, we propose a downlink channel estimation method, which jointly uses channel state information reference signal and demodulation reference signal. The simulation results show that the proposed multi-RB optimal precoding can effectively improve the downlink sum rate, and the proposed downlink channel estimation can obtain accurate multi-RB frequency-domain channel parameters.

High-Accuracy CSI Feedback With Super-Resolution Network for Massive MIMO Systems

Acquiring accurate channel state information (CSI) is critical for downlink precoding in frequency division duplexity (FDD) massive multiple-input multiple-output (MIMO) systems. In contrast to the traditional compressive sensing (CS) based methods, whose performance is hindered by excessive feedback overhead, this letter proposes a super-resolution network (SRNet) to compress and reconstruct the CSI. Specifically, the SRNet consists of encoder and decoder, where the encoder can transform channel matrices into codewords, and the decoder can restore different levels of spatial frequency features of CSI image based on a modified embedded block residual network (EBRN+). In addition, a principal component mark (PCM) method is proposed before encoding to lighten the encoder at UE. The experiment results show that our proposed model can achieve better performance than the state-of-the-art models with less training parameters and lower computational complexity at UE. Moreover, the superiority of our proposed model becomes much more significant especially under high compression ratio scenarios.

Secure Transmission Scheme Based on Fingerprint Positioning in Cell-Free Massive MIMO Systems

In this paper, we mainly study how to improve the secure transmission performance of cell-free massive multiple-input multiple-output (MIMO) systems by using location technology. In cell-free massive MIMO systems, active pilot attacks will contaminate the uplink channel estimation and affect the downlink precoding of access points (APs). In order to effectively reduce the impact of active pilot attacks on user transmission, this paper respectively proposes an user location estimation method based on fingerprint positioning and a channel estimation algorithm based on location information. Firstly, under the imperfect channel state information, the location information of users and eavesdropper is obtained by using fingerprint positioning method and K-means clustering algorithm. Then, combined with location information, AP selection strategy and channel estimation method based on non-overlapping angle of arrival (AOA) criterion are proposed respectively. Based on the location information of users and eavesdropper, we use discrete Fourier transform (DFT) to distinguish the uplink channels of legitimate user and eavesdropper from the angle domain, thus eliminating the pilot contamination caused by active pilot attacks. The results show that compared with the traditional transmission method, the proposed secure transmission strategy can increase the secrecy rate of up to 2 b/s/Hz, which effectively enhances the secure transmission performance of cell-free massive MIMO in strong interference environment.

On Channel Reciprocity in Reconfigurable Intelligent Surface Assisted Wireless Networks

Channel reciprocity greatly facilitates downlink precoding in time-division duplexing (TDD) multiple-input multiple-output (MIMO) communications without the need for channel state information (CSI) feedback. Recently, reconfigurable intelligent surfaces (RISs) emerge as a promising technology to enhance the performance of future wireless networks. However, since the artificial electromagnetic characteristics of RISs do not strictly follow the normal laws of nature, it brings up a question: does the channel reciprocity hold in RIS-assisted TDD wireless networks? After briefly reviewing the reciprocity theorem, in this article, we show that there still exists channel reciprocity for RIS-assisted wireless networks satisfying certain conditions. We also experimentally demonstrate the reciprocity at the sub-6 GHz and the millimeter-wave frequency bands by using two fabricated RISs. Furthermore, we introduce several RIS-assisted approaches to realizing nonreciprocal channels. Finally, potential opportunities brought by reciprocal/nonreciprocal RISs and future research directions are outlined.